I think that for many HTML tasks HTML::TokeParser is a good module, it is a slightly simpler interface to HTML::Parser. When you parse with HTML::Parser you have to have all of your handlers and logic set up before you can call parse(). But HTML::TokeParser will turn the entire HTML document into a stack of tokens that you can shift and unshift as needed. The tokens correspond to each element of your HTML page.

Because your program's logic is based on just a few criteria happening in an order, this is the perfect time for that. Here is some pseudocode that would use HTML::TokeParser:

#Get HTML Document
#HTML::TokeParser->new( HTML )
#get first Token
#until ( TokenTag eq 'h3' and TokenText eq 'foo')
#    get next Token
#if EndOfHTML then exit
#until ( TokenTag eq 'em' )
#    get next Token
#declare EM container
#until ( get TokenTag eq 'hr' )
#    add TokenText to EM container
#    get next Token
#use EM container
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As you can see, this logic is a lot simpler than trying to set up handlers for each of the tags you care about, then trying to manage states-- which is about what you have to do with HTML::Parser.